On envelopes of circle families in the plane

TL;DR

This paper explores the mathematical relationships between envelopes of circle families and various special curves in the plane, such as evolutes, pedals, evolutoids, and pedaloids, enhancing understanding of their geometric properties.

Contribution

It establishes new connections between circle envelopes and classical plane curves, providing insights into their geometric interactions.

Findings

Identified conditions linking circle envelopes to evolutes and pedals.

Derived properties of evolutoids and pedaloids related to circle families.

Enhanced geometric understanding of envelope-curves relationships.

Abstract

In this paper we investigate the relationships between envelopes of circle families and some special curves in the plane, such as evolutes, pedals, evolutoids and pedaloids.